Most household and construction debris is fine. Texas rules on what a landfill may accept set the outside limits.
A Texas landfill can't take lead-acid batteries, used motor oil, used oil filters, whole scrap tires, bulk liquids, or appliances with refrigerant that weren't handled properly. Whole tires can only be landfilled after they've been split or shredded, so pull them from the load.
The usual exclusions apply on our side as well. Hazardous waste, liquids, paint, solvents, fuel, and asbestos can't go in a standard dumpster.
A couple of local notes help. Dirt and clay are much heavier than they look, so a clay haul deserves its own small container. Your regular city cart service won't take construction material, which is exactly what a roll-off is built for.
Not sure about something? Ask your account manager before you load it.